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1 Motion – Newton’s Laws Gravity – A Closer Look The Universal law of Gravity

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2 Motion – Newton’s Laws Gravity – A Closer Look The Universal law of Gravity * Gravity is a force of attraction that acts between two massive object

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3 Motion – Newton’s Laws Gravity – A Closer Look The Universal law of Gravity * Gravity is a force of attraction that acts between two massive object * Two (massive) objects will exert a gravitational attraction with each other no matter how large or small the masses

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4 Motion – Newton’s Laws Gravity – A Closer Look The Universal law of Gravity * Gravity is a force of attraction that acts between two massive object * Two (massive) objects will exert a gravitational attraction with each other no matter how large or small the masses * Gravity is a fairly weak force unless the masses are quite large

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5 Motion – Newton’s Laws Gravity – A Closer Look The Universal law of Gravity * Gravity is a force of attraction that acts between two massive object * Two (massive) objects will exert a gravitational attraction with each other no matter how large or small the masses * Gravity is a fairly weak force unless the masses are quite large * First quantified by Newton

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6 Motion – Newton’s Laws Gravity – A Closer Look The Universal law of Gravity * Gravity is a force of attraction that acts between two massive object * Two (massive) objects will exert a gravitational attraction with each other no matter how large or small the masses * Gravity is a fairly weak force unless the masses are quite large * First quantified by Newton * Inverse square Law

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7 Motion – Newton’s Laws Gravity – A Closer Look The Universal law of Gravity * Gravity is a force of attraction that acts between two massive object * Two (massive) objects will exert a gravitational attraction with each other no matter how large or small the masses * Gravity is a fairly weak force unless the masses are quite large * First quantified by Newton * Inverse square Law * ‘Action at a Distance”

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Motion – Newton’s Laws Gravity – A Closer Look The Universal law of Gravity

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9 Motion – Newton’s Laws Gravity – A Closer Look The Universal law of Gravity m1m1 m2m2

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10 Motion – Newton’s Laws Gravity – A Closer Look The Universal law of Gravity m1m1 m2m2 r

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11 Motion – Newton’s Laws Gravity – A Closer Look The Universal law of Gravity F = G m 1 m 2 / r 2 m1m1 m2m2 r

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12 Motion – Newton’s Laws Gravity – A Closer Look The Universal law of Gravity F = G m 1 m 2 / r 2 G = 6.67 x N-m 2 / kg 2

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The Earth from Apollo 10

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15 Motion – Newton’s Laws Gravity – Why does g = 9/8 m/s 2 on the surface of the earth? F = G m 1 m 2 / r 2 m1m1 m2m2 r

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16 Motion – Newton’s Laws Gravity – Why does g = 9/8 m/s 2 on the surface of the earth? F = G m 1 m 2 / r 2 m1m1 m2m2 r

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17 Motion – Newton’s Laws Gravity – Why does g = 9/8 m/s 2 on the surface of the earth? F = G m 1 m 2 / r 2 Earth m1m1 m2m2 r r ≈ R earth m 1 = M earth

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18 Motion – Newton’s Laws Gravity – Why does g = 9/8 m/s 2 on the surface of the earth? F = G m 1 m 2 / r 2 = G M earth m 2 / R earth 2

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19 Motion – Newton’s Laws Gravity – Why does g = 9/8 m/s 2 on the surface of the earth? F = G m 1 m 2 / r 2 = G M earth m 2 / R earth 2 This is the force of gravity on m 2 and is, therefore, the weight of m 2.

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20 Motion – Newton’s Laws Gravity – Why does g = 9/8 m/s 2 on the surface of the earth? F = G m 1 m 2 / r 2 = G M earth m 2 / R earth 2 According tot the Second Law: F = G M earth m 2 / R earth 2 = m 2 a

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21 Motion – Newton’s Laws Gravity – Why does g = 9/8 m/s 2 on the surface of the earth? According to the Second Law: F = G M earth m 2 / R earth 2 = m 2 a Or, at the surface of the earth a = G M earth / R earth 2 = 9.8 m/s 2

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